Making a test available in more than one language versions has become a common practice in the fields of psychology and education. When comparisons of the populations taking the parent and the adapted versions of the test are to be made, the equivalence of the constructs of the tests must be established. Structural equations model (SEM) offers a unified approach for examining equivalences between the parent and adapted language version of a test by examining the equivalence of the constructs measured by the two versions of the test. While the procedures have the potential for yielding more direct information regarding whether the original and adapted version of an assessment instrument are equivalent, study investigating the power and type-I error rate of the procedures in the context of adaptation equivalence is not yet available. The present study is an attempt to fill this void. Three separate simulation studies were conducted to evaluate the effectiveness of the SEM approach for investigating test adaptation equivalence. In the first study the accuracy of the estimation procedure was investigated. In the second study, the Type-1 error rate of the procedure in identifying invariance in the parameters across two subgroups was investigated. In the third study, the power of the procedure in identifying differences in mean (Kappa) and structural (Lambda) parameters across two subgroups was investigated. The results of the first study indicated that the Kappa and Lambda parameters could be recovered with sufficient degree of accuracy with sample size in the order of 500. The Type I error rate for the Kappa and the lambda parameters were similar. With a sample size larger than 500, the Type I error rate approached the nominal levels. The power of the procedure in detecting differences increased with sample size and the magnitude of the difference in the parameters between the subgroups. With the kappa parameters, a sample of size 600 was required to detect a difference of .35 standardized units with a probability of .75. With the Lambda parameters, a difference of .2 in factor loading was detectable with a sample size of 300 with probability of .9.